Final answer:
Two vectors of different magnitudes cannot add up to zero, but three or more vectors can, even with different magnitudes, if they form a closed shape when connected head-to-tail.
Step-by-step explanation:
To answer the question of whether two vectors of different magnitudes can add to zero, the answer is no. Vectors add to zero only if they are of equal magnitude and opposite in direction. Hence, the fact that they have different magnitudes rules out the possibility of their resultant being zero.
However, when considering three or more vectors of different magnitudes, they can indeed add up to zero. This situation requires that the vectors are arranged such that they form a closed shape, typically a polygon, when connected head-to-tail. In this way, the overall displacement can be zero even though the magnitudes of the individual vectors are different.
So, in the context of the given options, the most accurate answer would be c) No, Yes - Their magnitudes must be equal for two vectors, but for three or more vectors, their magnitudes can be unequal and still sum to zero.